Longer geodesic lines on a mesh

Is there a way to achieve longer geodesic lines on a mesh ?
They fall from the top part because it always tries to find the shortest path, but I want them to follow the mesh curvature.

What is this?
Did you try something on grasshopper?
Can you attach some geometry?

If you made this with kangaroo, you can add pull to mesh forces and equal length to the segments of your “ropes” and it should give what you need.

Use Dodo for Grasshopper

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Thank you!